Multi-Dielectric Brownian Dynamics and Design-Space-Exploration Studies of Permeation in Ion Channels.

This paper proposes a multi-dielectric Brownian dynamics simulation framework for design-space-exploration (DSE) studies of ion-channel permeation. The goal of such DSE studies is to estimate the channel modeling-parameters that minimize the mean-squared error between the simulated and expected "permeation characteristics." To address this computational challenge, we use a methodology based on statistical inference that utilizes the knowledge of channel structure to prune the design space. We demonstrate the proposed framework and DSE methodology using a case study based on the KcsA ion channel, in which the design space is successfully reduced from a 6-D space to a 2-D space. Our results show that the channel dielectric map computed using the framework matches with that computed directly using molecular dynamics with an error of 7%. Finally, the scalability and resolution of the model used are explored, and it is shown that the memory requirements needed for DSE remain constant as the number of parameters (degree of heterogeneity) increases.

Brownian dynamics theory for predicting internal and external blockages of tetraethylammonium in the KcsA potassium channel.

The theory of Brownian dynamics is used to model permeation and the blocking of KcsA potassium channels by tetraethylammonium (TEA). A novel Brownian dynamics simulation algorithm is implemented that comprises two free energy profiles; one profile is seen by the potassium ions and the other by the TEA molecules whose shape is approximated by a sphere. Our simulations reveal that internally applied TEA blocks the passage of K(+) ions by physically occluding the pore. A TEA molecule in the external reservoir encounters an attractive energy-well created by four tyrosine residues at position 82, in addition to all other attractive and repulsive forces impinging on it. Using Brownian dynamics, we investigate how deep the energy-well needs to be to reproduce the experimentally determined inhibitory constant k(i) for the TEA blockade of KcsA or the mutant Shaker T449Y. The one-dimensional free energy profile obtained from molecular dynamics is first converted into a one-dimensional potential energy profile, and is then transformed into a three-dimensional free energy profile in Brownian dynamics by adding the short-range potential from the channel walls. When converted, the free energy profile calculated from molecular dynamics gives a well-depth of approximately 10 kT. We systematically alter the depths of the profiles, and then use Brownian dynamics simulations to numerically determine the current versus TEA-concentration curves. We show that the sequence of binding and unbinding events of the TEA molecule to the binding pocket can be modeled by a first-order Markov process. The Brownian dynamics simulations also reveal that the probability of a TEA molecule binding to the binding pocket in KcsA potassium channels increases exponentially with TEA concentration and depends also on the applied potential and the K(+) concentration in the simulation assembly.